OFFSET
0,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..431
Eric Weisstein's World of Mathematics, Laguerre Polynomial
Wikipedia, Laguerre polynomials
FORMULA
E.g.f.: exp(8*x/(1-x))/(1-x).
a(n) = n! * Sum_{i=0..n} 8^i/i! * binomial(n,i).
a(n) ~ exp(-4 + 4*sqrt(2*n) - n) * n^(n + 1/4) / 2^(5/4) * (1 + 451/(96*sqrt(2*n))). - Vaclav Kotesovec, Nov 13 2017
Sum_{n>=0} a(n) * x^n / (n!)^2 = exp(x) * Sum_{n>=0} 8^n * x^n / (n!)^2. - Ilya Gutkovskiy, Jul 17 2020
MAPLE
a:= n-> n! * add(binomial(n, i)*8^i/i!, i=0..n):
seq(a(n), n=0..20);
MATHEMATICA
Table[n!*LaguerreL[n, -8], {n, 0, 20}] (* Indranil Ghosh, Jul 04 2017 *)
PROG
(Python)
from mpmath import *
mp.dps=100
def a(n): return int(fac(n)*laguerre(n, 0, -8))
print([a(n) for n in range(21)]) # Indranil Ghosh, Jul 04 2017
(PARI) my(x = 'x + O('x^30)); Vec(serlaplace(exp(8*x/(1-x))/(1-x))) \\ Michel Marcus, Jul 04 2017
(PARI) a(n) = n!*pollaguerre(n, 0, -8); \\ Michel Marcus, Feb 05 2021
(Magma) m:=25; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Exp(8*x/(1-x))/(1-x))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, May 11 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 28 2017
STATUS
approved